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Simplifying x2 + 5x + 15 = (-1x2) + 4x Reorder the terms: 15 + 5x + x2 = (-1x2) + 4x Reorder the terms: 15 + 5x + x2 = 4x + (-1x2) Solving 15 + 5x + x2 = 4x + (-1x2) Solving for variable 'x'. 15 + 5x + x2 + -4x + x2 = 4x + (-1x2) + -4x + (x2) Reorder the terms: 15 + 5x + -4x + x2 + x2 = 4x + (-1x2) + -4x + (x2) Combine like terms: 5x + -4x = 1x 15 + 1x + x2 + x2 = 4x + (-1x2) + -4x + (x2) Combine like terms: x2 + x2 = 2x2 15 + 1x + 2x2 = 4x + (-1x2) + -4x + (x2) 15 + 1x + 2x2 = 4x + (-1x2) + -4x + x2 Reorder the terms: 15 + 1x + 2x2 = 4x + -4x + (-1x2) + x2 Combine like terms: 4x + -4x = 0 15 + 1x + 2x2 = 0 + (-1x2) + x2 15 + 1x + 2x2 = (-1x2) + x2 Combine like terms: (-1x2) + x2 = 0 15 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 0.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 0.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 0.5x + x2 = 0 + -7.5 0.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 0.5x + x2 = -7.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -7.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -7.5 + 0.0625 Combine like terms: -7.5 + 0.0625 = -7.4375 0.0625 + 0.5x + x2 = -7.4375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -7.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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